Greatest Common Factor of 564 and 567

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 564, 567 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 564 and 567 is 3.

GCF(564,567) = 3

GCF of 564 and 567

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 564 and 567

GCF of 564 and 567 is 3

Prime Factorization of 564


2 564
2 282
3 141
47 47
1

Prime factors of 564 are 2,3,47. Prime factorization of 564 in exponential form is:

564 = 22×31×471

Prime Factorization of 567


3 567
3 189
3 63
3 21
7 7
1

Prime factors of 567 are 3,7. Prime factorization of 567 in exponential form is:

567 = 34×71

∴ So by taking common prime factors GCF of 564 and 567 is 3

Greatest Common Factor of 564 and 567 by matching factors method

Factors of 564

List of positive integer factors of 564 that divides 564 without a remainder.

1,2,3,4,6,12,47,94,141,188,282,564

Factors of 567

List of positive integer factors of 567 that divides 567 without a remainder.

1,3,7,9,21,27,63,81,189,567

Greatest Common Factor

We found the factors and prime factorization of 564 and 567. The biggest common factor number is the GCF number.
So the greatest common factor 564 and 567 is 3.

Also check out the Least Common Multiple of 564 and 567

Properties of GCF 564 and 567

(i) The GCF of 564 and 567 is associative

GCF of 564 and 567 = GCF of 567 and 564

Related Greatest Common Factor of 564

Related Greatest Common Factor of 567

Frequently Asked Questions on GCF of 564 and 567

1. What is the GCF of 564 and 567?

Answer: GCF of 564 and 567 is 3.

2. What are the Factors of 564?

Answer: Factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564. There are 12 integers that are factors of 564. The greatest factor of 564 is 564.

3. What are the Factors of 567?

Answer: Factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567. There are 10 integers that are factors of 567. The greatest factor of 567 is 567.

4. How to Find the GCF of 564 and 567?

Answer:

Greatest Common Factor of 564 and 567 = 3

Step 1: Find the prime factorization of 564

564 = 2 x 2 x 3 x 47

Step 2: Find the prime factorization of 567

567 = 3 x 3 x 3 x 3 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 564 and 567 is 3